{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SQUDQ3HX7HCTPWCPPE76R53FL2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"179ae6533f54e987ec690b838d19853f03a3ab79c5683490c422a55241ad24bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-17T11:34:20Z","title_canon_sha256":"1428ad1d8ebba1880284ba00a8a31e6bb6be797752aefcf3cb5ca292e425afb9"},"schema_version":"1.0","source":{"id":"1801.05623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.05623","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.05623v1","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.05623","created_at":"2026-05-18T00:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"SQUDQ3HX7HCT","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SQUDQ3HX7HCTPWCP","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SQUDQ3HX","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:7c5e1a857fbc107b4d3b271b398042889d008b464b04caa3732f90df30678b2e","target":"graph","created_at":"2026-05-18T00:25:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2<p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\\pm\\infty$ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.","authors_text":"Du\\v{s}an D. Repov\\v{s}, Nikolaos S. Papageorgiou, Vicen\\c{t}iu D. R\\u{a}dulescu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-17T11:34:20Z","title":"Existence and multiplicity of solutions for resonant $(p,2)$-equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05623","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c6e3d3dc3f17651f85a380ddb6dd625e90f348b6a61483cd6101b2c9ec7c9c45","target":"record","created_at":"2026-05-18T00:25:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"179ae6533f54e987ec690b838d19853f03a3ab79c5683490c422a55241ad24bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-17T11:34:20Z","title_canon_sha256":"1428ad1d8ebba1880284ba00a8a31e6bb6be797752aefcf3cb5ca292e425afb9"},"schema_version":"1.0","source":{"id":"1801.05623","kind":"arxiv","version":1}},"canonical_sha256":"9428386cf7f9c537d84f793fe8f7655e9185dd8671e7797abaa9bd86864fefab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9428386cf7f9c537d84f793fe8f7655e9185dd8671e7797abaa9bd86864fefab","first_computed_at":"2026-05-18T00:25:40.686497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:40.686497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ynKwlF8XDKXaIECn7MhjQzPfn3vSGchJLw/+ZazP8049XG6O4AolpCQYmjZXjkA9Boq87nKNFVVUfuV/11HCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:40.687146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.05623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6e3d3dc3f17651f85a380ddb6dd625e90f348b6a61483cd6101b2c9ec7c9c45","sha256:7c5e1a857fbc107b4d3b271b398042889d008b464b04caa3732f90df30678b2e"],"state_sha256":"647f5ba4a64ed43aeead2d1a7fd5216bc7b3941bb402bfc299b862330ed983cc"}